Nanoscale imaging of equilibrium quantum Hall edge currents and of the magnetic monopole response in graphene

TL;DR

This study uses nanoscale imaging to explore equilibrium quantum Hall edge currents and magnetic monopole responses in graphene, revealing complex behaviors and counterpropagating currents that deepen understanding of topological states.

Contribution

It introduces a novel nanoscale imaging technique to directly observe equilibrium edge currents and magnetic monopole responses in graphene quantum Hall systems, uncovering previously unseen counterpropagating currents.

Findings

Observation of counterpropagating equilibrium currents at quantum Hall edges.

Direct imaging of magnetic monopole response in graphene.

Identification of complex nonlinear behaviors in topological and nontopological currents.

Abstract

The recently predicted topological magnetoelectric effect and the response to an electric charge that mimics an induced mirror magnetic monopole are fundamental attributes of topological states of matter with broken time reversal symmetry. Using a SQUID-on-tip, acting simultaneously as a tunable scanning electric charge and as ultrasensitive nanoscale magnetometer, we induce and directly image the microscopic currents generating the magnetic monopole response in a graphene quantum Hall electron system. We find a rich and complex nonlinear behavior governed by coexistence of topological and nontopological equilibrium currents that is not captured by the monopole models. Furthermore, by utilizing a tuning fork that induces nanoscale vibrations of the SQUID-on-tip, we directly image the equilibrium currents of individual quantum Hall edge states for the first time. We reveal that the edge states that are commonly assumed to carry only a chiral downstream current, in fact carry a pair of counterpropagating currents, in which the topological downstream current in the incompressible region is always counterbalanced by heretofore unobserved nontopological upstream current flowing in the adjacent compressible region. The intricate patterns of the counterpropagating equilibrium-state orbital currents provide new insights into the microscopic origins of the topological and nontopological charge and energy flow in quantum Hall systems.